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The existence of the exponentially stable limit cycle for a class of nonlinear systems. (English) Zbl 1197.34045
Summary: The exponentially stable limit cycle phenomenon for a class of nonlinear systems is investigated. Based on the analytic method, the existence and uniqueness of the exponentially stable limit cycle for such systems can be guaranteed. Moreover, the amplitude of oscillation, the period of oscillation, and guaranteed convergence rate can be correctly estimated. Finally, two numerical examples are provided to illustrate the use of the main result.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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